The previous two examples of QG models are minimal versions.
In particular, GR fits all observational and experimental tests for
a classical gravity [1]} and, in this sense, can be
regarded as a reference theory. On the contrary, there is not a
single experimental test for the fourth-derivative model of gravity
but, from another side, fourth derivative terms are required for the
renormalizability of semiclassical gravity. And the same model
guarantees also the renormalizability of QG [2]}. On
another hand, the fourth derivative theory has serious problems
related to nonphysical ghostsWhich have nothing to do
with the Faddeev-Popov ghosts, the traditional use of the same word
here is a mere coincidence. and stability, as we shall discuss
below. In this situation, one may look beyond the minimal theories
and it is natural to try the models with more than four derivatives.
Then, the number of derivatives may be finite or infinite. In the
first case we meet the polynomial in derivatives models of QG,
suggested in [3]}.
